Square-full numbers in Piatetski–Shapiro sequences

A positive integer n is called square-full if for every prime p|n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\vert n$$\end{document}, also p2|n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^2\vert n$$\end{document}. Piatetski–Shapiro sequences (PS-sequences) are defined by Nc=(⌊nc⌋)n∈N,(c>1,c∉N),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\mathbb {N}}^c=(\lfloor n^c \rfloor )_{n\in {\mathbb {N}}}, \quad (c>1, c\notin {\mathbb {N}}), \end{aligned}$$\end{document}where ⌊z⌋\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lfloor z\rfloor $$\end{document} is the integer part of a real z. In this paper we investigate the distribution of square-full numbers in Piatetski–Shapiro sequences.